Underwater Camera

This past year, my sister got an underwater camera for her birthday. She got a Panasonic Lumix waterproof digital camera that is designed to be waterproof up to 23 ft. Every summer, we go up to my uncle’s lake house on Lake George for a week. This past summer, we brought the camera and took some underwater pictures of fish, rocks, and our family. We didn’t pay much attention to the depth of the water because we only used it to a depth of about 4 ft.  I want to calculate the difference in pressure that the camera experiences when used at our average depth of 4 ft, vs. its maximum depth of 23 ft.

Pressure is equal to F / A which is also equal to phg where p is density, h is depth, and g is gravity. The density of freshwater is 1000 kg/m2. The total pressure is equal to PO + phg where PO is equal to atmospheric pressure. The formula for change in pressure is ΔP = Pf - Pi.

Pressure at 4 ft.

Pi = PO + pgh

Pi = (1.01 X 105 N/m2) + (1000 kg/m2)(4 ft)(9.8m/s2)(1m / 3.281 ft)

= 1.1 X 105  Pa

Pressure at 23 ft.

Pf = PO + pgh

Pf = (1.01 X 105 N/m2) + (1000 kg/m2)(23 ft)(9.8m/s2)(1m / 3.281 ft)

= 1.7 X 105  Pa

Change in Pressure

ΔP = Pf - Pi

 ΔP = 1.7 X 105  Pa - 1.1 X 105  Pa

= 60,000 Pa = 60 kPa

To put this into perspective, the world record for free-diving is 700 ft. This equates to around 2.2 X 106  Pa, almost 13 times more than what the camera can withstand.

Sources: https://www.nationalgeographic.com/news/2014/8/140810-free-diving-sperm-whales-jules-verne-reunion-booktalk/